Image completion via nonnegative matrix factorization using HALS and B-splines

When performing image completion, it is common to assume that images are smooth and low-rank, when viewed as matrices of pixel intensities. In this work, we use nonnegative matrix factorization to suc- cessively refine the image by representing alternatively rows and columns as smooth signals using splines. Previous work solved this model using an alternating direction method of multipliers. Instead, we propose to use a version of the hierarchical alternating least squares algorithm adapted to handle splines, and show in numerical experiments that it outperforms the existing method. Performance can be further improved by increasing progressively the size of used splines. We also introduce a non iterative algorithm using the same NMF approach, where factorization is computed in a fast and accurate way but for which convergence is harder to achieve.